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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Magnanimous-numbers/REXX/magnanimous-numbers.rexx Normal file
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/*REXX pgm finds/displays magnanimous #s (#s with a inserted + sign to sum to a prime).*/
parse arg bet.1 bet.2 bet.3 highP . /*obtain optional arguments from the CL*/
if bet.1=='' | bet.1=="," then bet.1= 1..45 /* " " " " " " */
if bet.2=='' | bet.2=="," then bet.2= 241..250 /* " " " " " " */
if bet.3=='' | bet.3=="," then bet.3= 391..400 /* " " " " " " */
if highP=='' | highP=="," then highP= 1000000 /* " " " " " " */
call genP /*gen primes up to highP (1 million).*/
do j=1 for 3 /*process three magnanimous "ranges". */
parse var bet.j LO '..' HI /*obtain the first range (if any). */
if HI=='' then HI= LO /*Just a single number? Then use LO. */
if HI==0 then iterate /*Is HI a zero? Then skip this range.*/
finds= 0; $= /*#: magnanimous # cnt; $: is a list*/
do k=0 until finds==HI /* [↓] traipse through the number(s). */
if \magna(k) then iterate /*Not magnanimous? Then skip this num.*/
finds= finds + 1 /*bump the magnanimous number count. */
if finds>=LO then $= $ k /*In range► Then add number ──► $ list*/
end /*k*/
say
say center(' 'LO "──►" HI 'magnanimous numbers ', 126, "─")
say strip($)
end /*j*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
magna: procedure expose @. !.; parse arg x 1 L 2 '' -1 R /*obtain #, 1st & last digit.*/
len= length(x); if len==1 then return 1 /*one digit #s are magnanimous*/
if x>1001 then if L//2 == R//2 then return 0 /*Has parity? Not magnanimous*/
do s= 1 for len-1 /*traipse thru #, inserting + */
parse var x y +(s) z; sum= y + z /*parse 2 parts of #, sum 'em.*/
if !.sum then iterate /*Is sum prime? So far so good*/
else return 0 /*Nope? Then not magnanimous.*/
end /*s*/
return 1 /*Pass all the tests, it's magnanimous.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13 /*assign low primes; # primes.*/
!.= 0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1 /* " semaphores to " */
#= 6; sq.#= @.# ** 2 /*# primes so far; P squared.*/
do j=@.#+4 by 2 to highP; parse var j '' -1 _; if _==5 then iterate /*÷ by 5?*/
if j// 3==0 then iterate; if j// 7==0 then iterate /*÷ by 3?; ÷ by 7?*/
if j//11==0 then iterate /*" " 11? " " 13?*/
do k=6 while sq.k<=j /*divide by some generated odd primes. */
if j//@.k==0 then iterate j /*Is J divisible by P? Then not prime*/
end /*k*/ /* [↓] a prime (J) has been found. */
#= #+1; @.#= j; sq.#= j*j; !.j= 1 /*bump #Ps; P──►@.assign P; P^2; P flag*/
end /*j*/; return